logit vs logistic regression

[#1]

What is the difference between using a logistic regression vs going through the generalized linear model fit using "logit?" Models are similar but I get slightly different values when I run the inverse prediction for my data. 

[#2]

They should be the same approach. Because the solution is found through maximum likelihood, which requires a search, you may get slightly different results for the parameter estimates. This could, in some situations, lead to different inverse prediction results.

The other major difference between the two could occur if you have categorical predictors. Generalized Regression uses a different coding scheme for categorical predictors than what is used with Fit Model.

[#3]

Thanks for explaining! Is there a way I can see the coding for the two fits to look at the differences between the calculations?

[#4]

From the JMP manuals (https://www.jmp.com/support/help/en/15.1/?os=win&source=application&utm_source=helpmenu&utm_medium=a... )

The parameterization of nominal variables used in the Generalized Regression personality
differs from their parameterization using other Fit Model personalities. The Generalized
Regression personality uses indicator function parameterization. In this parameterization, the
estimate that corresponds to the indicator for a level of a nominal variable is an estimate of the
difference between the mean response at that level and the mean response at the last level. The
last level is the level with the highest value order coding; it is the level whose indicator
function is not included in the model.

You should be able to see this by saving the prediction formulas to the data table and then looking at them. 

I should add that this parameterization should not affect the prediction. It will, of course, affect the parameter estimates.